More particularly, the invention relates to a controllable hydraulic vibration-damping support intended to be interposed for purposes of damping between first and second rigid elements, this vibration-damping support comprising:                first and second strength members intended to be secured to the two rigid elements to be connected, the first strength member having the form of a block and the second strength member being of annular shape centred on a central axis, the first strength member being arranged substantially on said central axis,        an elastomer body which connects together the first and second strength members and which delimits at least partially a working chamber, the elastomer body having a bell shape, having a top firmly fixed to the first strength member and an annular base firmly fixed to the second strength member,        a deformable compensation chamber which communicates with the working chamber via a constricted passageway, the compensation chamber, the working chamber and the first constricted passageway forming a hydraulic volume filled with liquid, the first constricted passageway having a resonance frequency comprised between 5 and 20 Hz,        an auxiliary chamber,        a decoupling valve comprising an isolating diaphragm made of elastomer, which separates the working chamber and the auxiliary chamber, said decoupling valve being adapted for absorbing vibrations at certain frequencies greater than 20 Hz,        a control device comprising an actuator adapted for selectively locking the isolating diaphragm.        Document EP-A-0115417 describes a vibration-damping support of this type, in which the auxiliary chamber, the decoupling valve and the control device are arranged at the level of the hydraulic compensation chamber.        